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Global Risk Management of Hedge Values and Arbitrage Opportunity

Please work problems; formula and showing how to solve problem are most important (so I can see how to solve similar problems). Thanks

American Airlines is trying to decide how to go about hedging â?¬70 million in ticket sales receivable in 180 days. Suppose it faces the following exchange and interest rates.
Spot rate: $0.6433-42/â?¬
Forward rate (180 days): $0.6578-99/â?¬
Euro 180-day interest rate (annualized): 4.01%-3.97%
U.S. dollar 180-day interest rate (annualized): 8.01%-7.98%

a. What is the hedged value of American's ticket sales using a forward market hedge?

b. What is the hedged value of American's ticket sales using a money-market hedge? Assume the first interest rate is the rate at which money can be borrowed and the second one the rate at which it can be lent.

c. Which hedge is less expensive?

d. Is there an arbitrage opportunity here?

e. Suppose the expected spot rate in 180 days is $0.67/â?¬, with a most likely range of $0.64-$0.70/â?¬. Should American hedge? What factors should enter into its decision

Solution Preview

a) The hedged value of American's ticket sales using a forward market hedge is 0.6578 x 70 million = $46.046 million. (We have used the forward rate for sellers)
b) The hedged value of American's ticket sales using a money market hedge is 70 million x 0.959 (remember the Euro -180- day interest for borrower is 4.10%) = 67.13. this needs to be multiplied by the spot rate for the seller of Euro that is 0.6433. = $43.184 million.
c) The forward market hedge is less expensive.
d) Yes. There is an arbitrage ...

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